scholarly journals Approximate Controllability of Semilinear Fractional Control Systems of Order α ∊ (1, 2]

2015 ◽  
pp. 175-180 ◽  
Author(s):  
Anurag Shukla ◽  
N. Sukavanam ◽  
D.N. Pandey
Keyword(s):  
Control Systems ◽  
Approximate Controllability ◽  
Fractional Control

scholarly journals Approximate Controllability of Fractional Integrodifferential Evolution Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
R. Ganesh ◽  
R. Sakthivel ◽  
N. I. Mahmudov ◽  
S. M. Anthoni
Keyword(s):  
Control System ◽  
Control Systems ◽  
Approximate Controllability ◽  
Evolution Equations ◽  
Semigroup Theory ◽  
Nonlocal Conditions ◽  
Sufficient Conditions ◽  
Approximately Controllable ◽  
Fractional Control ◽  
Lipschitz Conditions

This paper addresses the issue of approximate controllability for a class of control system which is represented by nonlinear fractional integrodifferential equations with nonlocal conditions. By using semigroup theory,p-mean continuity and fractional calculations, a set of sufficient conditions, are formulated and proved for the nonlinear fractional control systems. More precisely, the results are established under the assumption that the corresponding linear system is approximately controllable and functions satisfy non-Lipschitz conditions. The results generalize and improve some known results.

Approximate controllability of semilinear fractional differential systems of order 1 < q < 2 via resolvent operators

Filomat ◽  
2017 ◽  
Vol 31 (18) ◽  
pp. 5769-5781 ◽  
Author(s):  
Tingting Lian ◽  
Zhenbin Fan ◽  
Gang Li
Keyword(s):  
Control Systems ◽  
Approximate Controllability ◽  
Existence Results ◽  
Resolvent Operators ◽  
Differential Systems ◽  
Approximation Techniques ◽  
Fractional Differential Systems ◽  
Approximately Controllable ◽  
Fractional Differential ◽  
Fractional Control

Under a compactness assumption on the resolvent, some properties on relevant operators generated by resolvent are given. Existence results of fractional control systems are obtained by Schauder?s fixed point theorem and approximation techniques. Furthermore, the approximately controllable result is acquired under the assumption that the corresponding linear system is approximately controllable, which improves and extends some results on this topic.

Duality theory of fractional resolvents and applications to backward fractional control systems

2021 ◽  
Vol 24 (2) ◽  
pp. 541-558
Author(s):  
Shouguo Zhu ◽  
Gang Li
Keyword(s):  
Control System ◽  
Fractional Derivative ◽  
Control Systems ◽  
Diffusion Model ◽  
Duality Theory ◽  
Approximate Controllability ◽  
Fractional Diffusion ◽  
Variational Technique ◽  
Liouville Fractional Derivative ◽  
Fractional Control

Abstract We study the duality theory for fractional resolvents, extending and improving some corresponding theorems on semigroups. As applications, we develop the variational technique to analyze the finite-approximate controllability of a backward fractional control system with a right-sided Riemann-Liouville fractional derivative. Moreover, validity of our theoretical findings is given by a fractional diffusion model.

scholarly journals Results on the approximate controllability of fractional hemivariational inequalities of order $1< r<2$

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
M. Mohan Raja ◽  
V. Vijayakumar ◽  
Le Nhat Huynh ◽  
R. Udhayakumar ◽  
Kottakkaran Sooppy Nisar
Keyword(s):  
Fixed Point ◽  
Control Systems ◽  
Approximate Controllability ◽  
Hemivariational Inequalities ◽  
Evolution Inclusions ◽  
Fractional Systems ◽  
Cosine Families ◽  
Fixed Point Approach ◽  
Semilinear Control Systems ◽  
Theoretical Results

AbstractIn this paper, we investigate the approximate controllability of fractional evolution inclusions with hemivariational inequalities of order $1< r<2$ 1 < r < 2 . The main results of this paper are verified by using the fractional theories, multivalued analysis, cosine families, and fixed-point approach. At first, we discuss the existence of the mild solution for the class of fractional systems. After that, we establish the approximate controllability of linear and semilinear control systems. Finally, an application is presented to illustrate our theoretical results.

scholarly journals Approximate Controllability of Sobolev Type Nonlocal Fractional Stochastic Dynamic Systems in Hilbert Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Mourad Kerboua ◽  
Amar Debbouche ◽  
Dumitru Baleanu
Keyword(s):  
Control Systems ◽  
Hilbert Spaces ◽  
Dynamic Systems ◽  
Approximate Controllability ◽  
Dynamic Control ◽  
Sufficient Conditions ◽  
Sobolev Type ◽  
Stochastic Dynamic ◽  
Deterministic Control ◽  
Stochastic Dynamic Systems

We study a class of fractional stochastic dynamic control systems of Sobolev type in Hilbert spaces. We use fixed point technique, fractional calculus, stochastic analysis, and methods adopted directly from deterministic control problems for the main results. A new set of sufficient conditions for approximate controllability is formulated and proved. An example is also given to provide the obtained theory.

scholarly journals Approximate controllability of delayed semilinear control systems

2005 ◽  
Vol 2005 (1) ◽  
pp. 67-76 ◽  
Author(s):  
Lianwen Wang
Keyword(s):  
Differential Equations ◽  
Control Systems ◽  
Approximate Controllability ◽  
Sufficient Conditions ◽  
Semilinear Control Systems

We deal with the approximate controllability of control systems governed by delayed semilinear differential equations y˙(t)=Ay(t)+A1y(t−Δ)+F(t,y(t),yt)+(Bu)(t). Various sufficient conditions for approximate controllability have been obtained; these results usually require some complicated and limited assumptions. Results in this paper provide sufficient conditions for the approximate controllability of a class of delayed semilinear control systems under natural assumptions.

Approximate controllability of non-instantaneous impulsive semilinear measure driven control system with infinite delay via fundamental solution

2020 ◽  
Author(s):  
Surendra Kumar ◽  
Syed Mohammad Abdal
Keyword(s):  
Fundamental Solution ◽  
Differential Equations ◽  
Control Systems ◽  
Approximate Controllability ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Existence Of A Solution ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
New Class

Abstract This article investigates a new class of non-instantaneous impulsive measure driven control systems with infinite delay. The considered system covers a large class of the hybrid system without any restriction on their Zeno behavior. The concept of measure differential equations is more general as compared to the ordinary impulsive differential equations; consequently, the discussed results are more general than the existing ones. In particular, using the fundamental solution, Krasnoselskii’s fixed-point theorem and the theory of Lebesgue–Stieltjes integral, a new set of sufficient conditions is constructed that ensures the existence of a solution and the approximate controllability of the considered system. Lastly, an example is constructed to demonstrate the effectiveness of obtained results.

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